Correct Answer: D. injections

Correct Answer: B. metamorphosis

Correct Answer: B. board

Correct Answer: B. udder

Correct Answer: B) B

Explanation

(a) The position vector of L, \(\overrightarrow{OL} = 5i + 6j\)

The coordinates of L = (5, 6)

The position vector of M, \(\overrightarrow{OM} = 13i + 4j\)

The coordinates of M = (13, 4).

Let \(\overrightarrow{OK} = xi + yj\) be the position vector of K.

\(\overrightarrow{LK} = (x - 5)i + (y - 6)j\), \(\overrightarrow{KM} = (13 - x)i + (4 - y)j\)

\(LK : KM = 2 : 3 ; \frac{LK}{KM} = \frac{2}{3}\)

\(3[(x - 5)i + (y - 6)j] = 2[(13 - x)i + (4 - y)j]\)

Equating by components,

\(i : 3x - 15 = 26 - 2x \implies 5x = 41\)

\(x = \frac{41}{5}\)

\(j : 3y - 18 = 8 - 2y \implies 5y = 26\)

\(y = \frac{26}{5}\)

The position vector of K is \(\overrightarrow{OK} = \frac{41}{5} i + \frac{26}{5} j\)

(b) \(\overrightarrow{AC} = \overrightarrow{AB} + \overrightarrow{BC}\)

= \(\begin{pmatrix} 8 \cos 60° \\ 8 \sin 60° \end{pmatrix} + \begin{pmatrix} 12 \cos 130° \\ 12 \sin 130° \end{pmatrix}\)

= \(\begin{pmatrix} 8 \times \frac{1}{2} \\ 8 \times \frac{\sqrt{3}}{2} \end{pmatrix} + \begin{pmatric} -12 \times 0.6428 \\ 12 \times 0.7660 \end{pmatrix}\)

= \(\begin{pmatrix} 4 \\ 4\sqrt{3} \end{pmatrix} + \begin{pmatrix} -7.7136 \\ 9.9192 \end{pmatrix} = \begin{pmatrix} -3.7136 \\ 16.12 \end{pmatrix}\)

\(|AC| = \sqrt{(-3.7136)^{2} + (16.12)^{2}} = \sqrt{13.794 + 259.9}\)

= \(\sqrt{273.694} = 16.544 \approxeq 16.5 km\)

\(AB = (8 \cos 60 i + 8 \sin 60 j) ; AC = (-3.7136 i + 16.12 j)\)

(ii)

Let the angle between \(\overrightarrow{AB}\) and \(\overrightarrow{AC}\) be \(\theta\).

Using sine rule,

\(\frac{\sin B}{AC} = \frac{\sin A}{BC}\)

\(\frac{\sin 110°}{16.5} = \frac{\sin \theta}{12}\)

\(\sin \theta = \frac{12 \sin 110°}{16.5}\)

\(\sin \theta = 0.6834\)

\(\theta = \sin^{-1} (0.6834) = 43.11°\)

Bearing of C from A = 60° + 43.11° = 103.11° \(\approxeq\) 103° (nearest degree)

Correct Answer: A. brink

Correct Answer: C. Cell

Explanation

(a) The economic importance of insect pests in crop production are: (i) They destroy crops on the field through their sucking, burrowing and defoliation activities. (ii) They reduce the yield and in some cases attack may lead to total crop failure. (iii) They reduce the nutritional value of crops either on the field or in store. (iv) Farmers' profits are drastically reduced. (v) Cost of production is increased as large sum of money is expended on their control. (vi) They render ' vegetables and fruits unattractive and unmarketable. (vii) They reduce viability of stored seeds. (viii) They serve as , vectors of diseases. (ix) Some are agents of pollination. (x) The wounds they create while feeding on plants predispose plants to infection.

(b) Hosts of cotton stainer are: (i) kenaf (ii) Okra (iii) silk cotton tree

(c) Soil-living insect pest of crops include: (rickets and termites. Control measures of insect pest of crops are: i) use of resistant or tolerant varieties, (ii) crop rotation practices, (iii) spraying crops with insecticides. (iv) dusting seeds or planting materials with powdered insecticides e.g. aldrin dust (seed treatment), (v) tillage practices. (vi) timely planting of crops; (vii) timely harvesting, (viii) farm hygiene / sanitation.

Correct Answer: B. it is the average mass of all the isotopes of the element